Kolyvagin systems and Iwasawa theory of generalized Heegner cycles

Abstract

Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne's p-adic representation attached to a modular form of even weight >2. In this setting, the role of Heegner points is played by higher-dimensional Heegner-type cycles that have been recently defined by Bertolini, Darmon and Prasanna. Our results should be compared with those obtained, via deformation-theoretic techniques, by Fouquet in the context of Hida families of modular forms.

arXiv comment20 pages

References in corpus (1)

• Variation of Heegner points in Hida families

Cited by in corpus (4)

• Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II
• Indivisibility of Heegner cycles over Shimura curves and Selmer groups
• On the structure of the Bloch--Kato Selmer groups of modular forms over anticyclotomic ${\mathbf{Z}}_p$-towers
• On anticyclotomic Euler and Kolyvagin systems